Question

ABCD is a rhombus with AB = 13 cm. If OB = 5 cm then what is the length of the diagonal AC?​

Answer 1

Answer:

ANSWER

In a rhombus, diagonals are perpendicular to each other and bisect each other.

∴BO=OD=12cm

∴y=12cm

and

CO=OA=5cm

∴x=5cm

Since BC

2

=CO

2

+BO

2

, by substituting values we get:

BC

2

=(12)

2

+(5)

2

⇒BC=

169

⇒BC=13cm

Since all sides are equal, BC=CD

∴z=13cm

Hence, the value of x is 5cm and the value of z is 13cm.

Step-by-step explanation:

i hope it will help you

Answer 2

Answer:

Given =  ABCD is a rhombus in which AB = BC = CD = DA = 13 cm OB = 5 cm

To Find = Length of Diagonal AC

We know that Diagonals of Rhombus bisects each other at 90

In Triangle BOC we have

Angle BOC = 90 ( because Diagonals OF a rhombus bisects each other at 90)  

OB = 5cm (Given)

BC = 13cm (Given)

According to Pythagoreas Theorem We have,

(Hypotnuse)^2 = (Height)^2 + (Base)^2

(BC)^2 = (OB)^2 + (OC)^2

(13)^2 = (5)^2 + (OC)^2

169 = 25 + (OC)^2

169 - 25 = (OC)^2

144 = (OC)^2

$\sqrt{144} = OC$

12 = OC

AC = 2(OC)

AC = 2*12

AC = 24 cm